While I am asking, what is the best soil mixture for growing these peppers..

They are about 1 1/4 inch tall right now.. Only 2 leaves. I would like to transplant them into a 2 gallon pot. Hope this is big enough for the plant to produce peppers.

Two true leaves are good to transplant, while its not ideal to use a two gallon pot for a final home they will produce peppers. You will probably experience tipping, when I planted in smaller pots the pepper plants became so top heavy I had to use bricks and rocks around them to hold in place. Larger is always better if you can, if not go with what you have.

I have access to larger tubs. Thanks for the advise..

5 gallon pots are a good size. 3 is usually considered minimum and for most peppers, anything over 7 or 8 is usually over doing it. At least that is my non-professional opinion.

Sounds like you are well in your way to transplanting and keep us updated on their progress.